I'm mostly a Standard Theory guy, though I'd modify it a bit to say that the memories and desires of the original person drive the vampire. But once Joss adopted the soul for Angel he had to bring in a form of essentialism, and that means the vampire differs in some essential way from the original. Restoring the soul means the same: the newly souled creature is not "the same" as the vampire.
I think part of what drives the dispute is the different thematic needs of BtVS and AtS. Essentialism is an essential (sorry) part of the storyline in S1-3 of BtVS. In contrast, for Angel's redemption quest to have any meaning on AtS, the presence or absence of the soul can't make any real difference (or else Angel would bear no actual responsibility for the crimes of Angelus). I resolve this by treating the 2 shows as different, so that we shouldn't take the themes of one and try to apply them to the other. I think I'm in a distinct minority on this, but it works for me.
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I think part of what drives the dispute is the different thematic needs of BtVS and AtS. Essentialism is an essential (sorry) part of the storyline in S1-3 of BtVS. In contrast, for Angel's redemption quest to have any meaning on AtS, the presence or absence of the soul can't make any real difference (or else Angel would bear no actual responsibility for the crimes of Angelus). I resolve this by treating the 2 shows as different, so that we shouldn't take the themes of one and try to apply them to the other. I think I'm in a distinct minority on this, but it works for me.